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Mette B. Gaarde

Publications and source records attributed to Mette B. Gaarde.

At least 37 records · Page 2Linked to original sources

Polarization-control of absorption of virtual dressed-states in helium

The extreme ultraviolet absorption spectrum of an atom is strongly modified in the presence of a synchronized intense infrared field. In this work we demonstrate control of the absorption properties of helium atoms dressed by an infrared pulse by changing the relative polarization of the infrared and extreme ultraviolet fields. Light-induced features associated with the dressed $1s2s$, $1s3s$ and $1s3d$ states, referred to as $2s^{+}$, $3s^{\pm}$ and $3d^{\pm}$ light induced states, are shown to be strongly modified or even eliminated when the relative polarization is rotated. The experimental results agree well with calculations based on the solution of the time-dependent Schrödinger equation using a restricted excitation model that allows efficient treatment of the three dimensional problem. We also present an analysis of the light induced states based on Floquet theory, which allows for a simple explanation of their properties. Our results open a new route to creating controllable superpositions of dipole allowed and non-dipole allowed states in atoms and molecules.

physics.optics↗

Phase Control of Attosecond Pulses in a Train

Ultrafast processes in matter can be captured and even controlled by using sequences of few-cycle optical pulses, which need to be well characterized, both in amplitude and phase. The same degree of control has not yet been achieved for few-cycle extreme ultraviolet pulses generated by high-order harmonic generation in gases, with duration in the attosecond range. Here, we show that by varying the spectral phase and carrier-envelope phase (CEP) of a high-repetition rate laser, using dispersion in glass, we achieve a high degree of control of the relative phase and CEP between consecutive attosecond pulses. The experimental results are supported by a detailed theoretical analysis based upon the semiclassical three-step model for high-order harmonic generation.

physics.atom-ph↗

Spatio-temporal coupling of attosecond pulses

The shortest light pulses produced to date are of the order of a few tens of attoseconds, with central frequencies in the extreme ultraviolet range and bandwidths exceeding tens of eV. They are often produced as a train of pulses separated by half the driving laser period, leading in the frequency domain to a spectrum of high, odd-order harmonics. As light pulses become shorter and more spectrally wide, the widely-used approximation consisting in writing the optical waveform as a product of temporal and spatial amplitudes does not apply anymore. Here, we investigate the interplay of temporal and spatial properties of attosecond pulses. We show that the divergence and focus position of the generated harmonics often strongly depend on their frequency, leading to strong chromatic aberrations of the broadband attosecond pulses. Our argumentation uses a simple analytical model based on Gaussian optics, numerical propagation calculations and experimental harmonic divergence measurements. This effect needs to be considered for future applications requiring high quality focusing while retaining the broadband/ultrashort characteristics of the radiation.

physics.optics↗

Ab-initio calculations of the linear and nonlinear susceptibilities of N$_2$, O$_2$, and air in the mid-infrared

We present first-principles calculations of the linear and nonlinear susceptibilities of N$_2$, O$_2$, and air in the mid-infrared wavelength regime, from $1-4$ $μ$m. We extract the frequency-dependent susceptibilities from the full time-dependent dipole moment that is calculated using time-dependent density functional theory. We find good agreement with curves derived from experimental results for the linear susceptibility, and with measurements for the nonlinear susceptibility up to 2.4 $μ$m. We also find that the susceptibilities are insensitive to the laser intensity even in the strong field regime up to $5\times 10^{13}$ W/cm$^2$. Our results will allow accurate calculations of the long-distance propagation of intense MIR laser pulses in air.

physics.optics↗

Controlled free-induction decay in the extreme ultraviolet

Coherent sources of attosecond extreme ultraviolet (XUV) radiation present many challenges if their full potential is to be realized. While many applications benefit from the broadband nature of these sources, it is also desirable to produce narrow band XUV pulses, or to study autoionizing resonances in a manner that is free of the broad ionization background that accompanies above-threshold XUV excitation. Here we demonstrate a method for controlling the coherent XUV free induction decay that results from using attosecond pulses to excite a gas, yielding a fully functional modulator for XUV wavelengths. We use an infrared (IR) control pulse to manipulate both the spatial and spectral phase of the XUV emission, sending the light in a direction of our choosing at a time of our choosing. This allows us to tailor the light using opto-optical modulation, similar to devices available in the IR and visible wavelength regions.

physics.atom-ph↗

Role of Excited States In High-order Harmonic Generation

We investigate the role of excited states in High-order Harmonic Generation by studying the spectral, spatial and temporal characteristics of the radiation produced near the ionization threshold of argon by few-cycle laser pulses. We show that the population of excited states can lead either to direct XUV emission through Free Induction Decay or to the generation of high-order harmonics through ionization from these states and recombination to the ground state. By using the attosecond lighthouse technique, we demonstrate that the high-harmonic emission from excited states is temporally delayed by a few femtoseconds compared to the usual harmonics, leading to a strong nonadiabatic spectral redshift.

physics.atom-ph↗

Multi-level perspective on high-order harmonic generation in solids

We investigate high-order harmonic generation in a solid, modeled as a multi-level system dressed by a strong infrared laser field. We show that the cutoff energies and the relative strengths of the multiple plateaus that emerge in the harmonic spectrum can be understood both qualitatively and quantitatively by considering a combination of adiabatic and diabatic processes driven by the strong field. Such a model was recently used to interpret the multiple plateaus exhibited in harmonic spectra generated by solid argon and krypton [Ndabashimiye {\it et al.}, Nature 534, 520 (2016)]. We also show that when the multi-level system originates from the Bloch state at the $Γ$ point of the band structure, the laser-dressed states are equivalent to the Houston states [Krieger {\it el al.} Phys. Rev. B 33, 5494 (1986)] and will therefore map out the band structure away from the $Γ$ point as the laser field increases. This leads to a semi-classical three-step picture in momentum space that describes the high-order harmonic generation process in a solid.

quant-ph↗

Attosecond Transient Absorption in Dense Gases: Exploring the Interplay between Resonant Pulse Propagation and Laser-Induced Line Shape Control

We investigate the evolution of extreme ultraviolet (XUV) spectral lineshapes in an optically-thick helium gas under near-infrared (IR) perturbation. In our experimental and theoretical work, we systematically vary the IR intensity, time-delay, gas density and IR polarization parameters to study lineshape modifications induced by collective interactions, in a regime beyond the single atom response of a thin, dilute gas. In both experiment and theory, we find that specific features in the frequency-domain absorption profile, and their evolution with propagation distance, can be attributed to the interplay between resonant attosecond pulse propagation and IR induced phase shifts. Our calculations show that this interplay also manifests itself in the time domain, with the IR pulse influencing the reshaping of the XUV pulse propagating in the resonant medium.

physics.atom-ph↗

Semi-Classical Wavefunction Perspective to High-Harmonic Generation

We introduce a semi-classical wavefunction (SCWF) model for strong-field physics and attosecond science. When applied to high harmonic generation (HHG), this formalism allows one to show that the natural time-domain separation of the contribution of ionization, propagation and recollisions to the HHG process leads to a frequency-domain factorization of the harmonic yield into these same contributions, for any choice of atomic or molecular potential. We first derive the factorization from the natural expression of the dipole signal in the temporal domain by using a reference system, as in the quantitative rescattering (QRS) formalism [J. Phys. B. 43, 122001 (2010)]. Alternatively, we show how the trajectory component of the SCWF can be used to express the factorization, which also allows one to attribute individual contributions to the spectrum to the underlying trajectories.

physics.atom-ph↗

The interplay between resonant enhancement and quantum path dynamics in harmonic generation in helium

We present a theoretical study of the influence of resonant enhancement on quantum path dynamics in the generation of harmonics above and below the ionization threshold in helium. By varying the wavelength and intensity of the driving field from 425 nm to 500 nm and from 30 TW/cm${^2}$ to 140 TW/cm${^2}$, respectively, we identify enhancements of harmonics 7, 9, and 11 that correspond to multiphoton resonances between the ground state and the Stark shifted $1s2p$, $1s3p$, and $1s4p$ excited states. A time-frequency analysis of the emission shows that both the short and long quantum path contributions to the harmonic yield are enhanced through these bound state resonances. We analyze the sub-cycle time structure of the 9th harmonic yield in the vicinity of the resonances and find that on resonance the long trajectory contribution is phase shifted by approximately $π/4$. Finally, we compare the single atom and the macroscopic response of a helium gas and find that while the sub-cycle time profiles are slightly distorted by propagation effects, the phase shift of the long trajectory contribution is still recognizable.

physics.atom-ph↗

Beyond the single-atom response in absorption lineshapes: Probing a dense, laser-dressed helium gas with attosecond pulse trains

We investigate the absorption line shapes of laser-dressed atoms beyond the single-atom response, by using extreme ultraviolet (XUV) attosecond pulse trains to probe an optically thick helium target under the influence of a strong infrared (IR) field. We study the interplay between the IR-induced phase shift of the microscopic time-dependent dipole moment and the resonant-propagation-induced reshaping of the macroscopic XUV pulse. Our experimental and theoretical results show that as the optical depth increases, this interplay leads initially to a broadening of the IR-modified line shape, and subsequently to the appearance of new, narrow features in the absorption line.

physics.atom-ph↗

High harmonic generation from Bloch electrons in solids

We study the generation of high harmonic radiation by Bloch electrons in a model transparent solid driven by a strong mid-infrared laser field. We solve the single-electron time-dependent Schrödinger equation (TDSE) using a velocity-gauge method [New J. Phys. 15, 013006 (2013)] that is numerically stable as the laser intensity and number of energy bands are increased. The resulting harmonic spectrum exhibits a primary plateau due to the coupling of the valence band to the first conduction band, with a cutoff energy that scales linearly with field strength and laser wavelength. We also find a weaker second plateau due to coupling to higher-lying conduction bands, with a cutoff that is also approximately linear in the field strength. To facilitate the analysis of the time-frequency characteristics of the emitted harmonics, we also solve the TDSE in a time-dependent basis set, the Houston states [Phys. Rev. B 33, 5494 (1986)], which allows us to separate inter-band and intra-band contributions to the time-dependent current. We find that the inter-band and intra-band contributions display very different time-frequency characteristics. We show that solutions in these two bases are equivalent under an unitary transformation but that, unlike the velocity gauge method, the Houston state treatment is numerically unstable when more than a few low lying energy bands are used.

physics.atom-ph↗

Multiphoton transitions for delay-zero calibration in attosecond spectroscopy

The exact delay-zero calibration in an attosecond pump-probe experiment is important for the correct interpretation of experimental data. In attosecond transient absorption spectroscopy the determination of the delay-zero exclusively from the experimental results is not straightforward and may introduce significant errors. Here, we report the observation of quarter-laser-cycle (4ω) oscillations in a transient absorption experiment in helium using an attosecond pulse train overlapped with a precisely synchronized, moderately strong infrared pulse. We demonstrate how to extract and calibrate the delay-zero with the help of the highly nonlinear 4ω signal. A comparison with the solution of the time-dependent Schrödinger equation is used to confirm the accuracy and validity of the approach. Moreover, we study the mechanisms behind the quarter-laser-cycle and the better-known half-laser-cycle oscillations as a function of experimental parameters. This investigation yields an indication of the robustness of our delay-zero calibration approach.

physics.atom-ph↗

Quantum interference in attosecond transient absorption of laser-dressed helium atoms

We calculate the transient absorption of an isolated attosecond pulse by helium atoms subject to a delayed infrared (\ir) laser pulse. With the central frequency of the broad attosecond spectrum near the ionization threshold, the absorption spectrum is strongly modulated at the sub-\ir-cycle level. Given that the absorption spectrum results from a time-integrated measurement, we investigate the extent to which the delay-dependence of the absorption yields information about the attosecond dynamics of the atom-field energy exchange. We find two configurations in which this is possible. The first involves multi photon transitions between bound states that result in interference between different excitation pathways. The other involves the modification of the bound state absorption lines by the IR field, which we find can result in a sub-cycle time dependence only when ionization limits the duration of the strong field interaction.

physics.atom-ph↗

Laser-induced bound-state phases in high-order harmonic generation

We present single-molecule and macroscopic calculations showing that laser-induced Stark shifts contribute significantly to the phase of high-order harmonics from polar molecules. This is important for orbital tomography, where phases of field-free dipole matrix elements are needed in order to reconstruct molecular orbitals. We derive an analytical expression that allows the first-order Stark phase to be subtracted from experimental measurements.

quant-ph↗

Two-center minima in harmonic spectra from aligned polar molecules

We extend a model of two-center interference to include the superposition of opposite orientations in aligned polar molecules. We show that the position of the minimum in the harmonic spectrum from both aligned and oriented CO depends strongly on the relative recombination strength at different atoms, not just the relative phase. We reinterpret the minimum in aligned CO as an interference between opposite orientations, and obtain good agreement with numerical calculations. Inclusion of the first-order Stark effect shifts the position of the interference minimum in aligned CO even though aligned molecules do not posses total permanent dipoles. We explain the shift in terms of an extra phase that the continuum electron of oriented CO accumulates due to the Stark effect.

physics.atom-ph↗

Transient absorption and reshaping of ultrafast XUV light by laser-dressed helium

We present a theoretical study of transient absorption and reshaping of extreme ultraviolet (XUV) pulses by helium atoms dressed with a moderately strong infrared (IR) laser field. We formulate the atomic response using both the frequency-dependent absorption cross section and a time-frequency approach based on the time-dependent dipole induced by the light fields. The latter approach can be used in cases when an ultrafast dressing pulse induces transient effects, and/or when the atom exchanges energy with multiple frequency components of the XUV field. We first characterize the dressed atom response by calculating the frequency-dependent absorption cross section for XUV energies between 20 and 24 eV for several dressing wavelengths between 400 and 2000 nm and intensities up to 10^12 W/cm^2. We find that for dressing wavelengths near 1600 nm, there is an Autler-Townes splitting of the 1s ---> 2p transition that can potentially lead to transparency for absorption of XUV light tuned to this transition. We study the effect of this XUV transparency in a macroscopic helium gas by incorporating the time-frequency approach into a solution of the coupled Maxwell-Schrödinger equations. We find rich temporal reshaping dynamics when a 61 fs XUV pulse resonant with the 1s ---> 2p transition propagates through a helium gas dressed by an 11 fs, 1600 nm laser pulse.

physics.atom-ph↗

VUV frequency combs from below-threshold harmonics

Recent demonstrations of high-harmonic generation (HHG) at very high repetition frequencies (~100 MHz) may allow for the revolutionary transfer of frequency combs to the vacuum ultraviolet (VUV). This advance necessitates unifying optical frequency comb technology with strong-field atomic physics. While strong-field studies of HHG have often focused on above-threshold harmonic generation (photon energy above the ionization potential), for VUV frequency combs an understanding of below-threshold harmonic orders and their generation process is crucial. Here we present a new and quantitative study of the harmonics 7-13 generated below and near the ionization threshold in xenon gas. We show multiple generation pathways for these harmonics that are manifested as on-axis interference in the harmonic yield. This discovery provides a new understanding of the strong-field, below-threshold dynamics under the influence of an atomic potential and allows us to quantitatively assess the achievable coherence of a VUV frequency comb generated through below threshold harmonics. We find that under reasonable experimental conditions temporal coherence is maintained. As evidence we present the first explicit VUV frequency comb structure beyond the 3rd harmonic.

physics.atom-ph↗